The Nature of Narrow Content[*]

*[[The material here overlaps a little with the earlier
sections of "The Components of Content" (Chalmers 2002b), the later
sections of which provide further details on the analysis and
application of the notion of narrow content developed here, and relate
it to other accounts of narrow content that have been proposed. Also
relevant are "The Nature of Epistemic Space" (Chalmers forthcoming b),
which develops the foundational ideas about epistemic possibility and
the space of scenarios, and "The Foundations of Two-Dimensional
Semantics" (Chalmers forthcoming a), which situates this approach as a
variety of two-dimensional semantics and fills in many further details
that are passed over here.]]

1 Introduction

A
content of a subject's mental state is narrow when it is
determined by the subject's intrinsic properties: that is, when any
possible intrinsic duplicate of the subject has a corresponding mental
state with the same content. A content of a subject's mental state is
wide when it depends in part on the subject's extrinsic
properties: that is, when there is a possible intrinsic duplicate of
the subject whose corresponding mental state lacks this content.

It is commonly accepted that many mental states have wide content.
For example, where Oscar on Earth believes that water is wet, his
intrinsic duplicate Twin Oscar on Twin Earth (just like Earth, except
that H2O is replaced by the superficially identical XYZ) does not: he
believes that twin water is wet.[*] Further, it appears that Oscar and
Twin Oscar have corresponding beliefs with different truth-conditions:
Oscar's belief is true of worlds where H2O is wet, while Twin Oscar's
belief is true of worlds where XYZ is wet. So insofar as these belief
ascriptions and truth-conditions reflect the beliefs' contents, those
contents are wide.

*[[Putnam 1975, as adapted by
McGinn 1977 and Burge 1982.]]

The existence of wide content
is compatible in principle with the hypothesis that every mental state
has narrow content: that is, that there is a (different) sort of
content such that corresponding mental states of intrinsic duplicates
have the same content of this sort. This hypothesis has intuitive
appeal, but it has proven difficult to explicate an acceptable notion
of narrow content. On my view, to understand narrow content, one must
ground the notion in epistemic terms. In this paper I develop an
account of this sort.

2 Epistemic space

I will be
centrally concerned with propositional attitudes with a mind-to-world
direction of fit: believing that P, expecting that P, hypothesizing
that P, and so on. Let us call the most general propositional
attitude in this class thought: so when one believes or expects
or hypothesizes that P, one thinks that P. Let us say that a thought
is an occurrent propositional attitude token of this type: roughly, an
entertaining of a given content. Then a thought aims to represent the
world, and can be assessed for truth or falsity. Note that understood
this way, thoughts are tokens rather than types.

The account I
will give will be grounded in a basic notion of the epistemic
necessity of thoughts. This notion can be understood in various
ways, but on the account I prefer, epistemic necessity is understood
in terms of apriority. We can say that a thought is epistemically
necessary when it can be justified independently of experience,
yielding a priori knowledge. We can then say that a thought is
epistemically possible when the negation of the thought is not
epistemically necessary.[*] Epistemic possibility corresponds to
rational coherence, on idealized a priori reflection.

*[[To handle cases of a priori indeterminacy, it is arguably
better to say that a thought T is epistemically possible when ~det(T)
is not epistemically necessary, where det(T) is a thought that is true
when T is determinately true and false when T is false or
indeterminate; and ~det(T) is its negation. I will abstract away from
concerns about indeterminacy in what follows.]]

It is a
common intuitive idea that when a thought is epistemically possible,
there are specific epistemically possible scenarios that the
thought endorses. In effect, any thought divides the space of
scenarios into a class of scenarios that the thought endorses, and the
class of scenarios that the thought excludes. When both a thought and
its negation are epistemically possible, there will be scenarios in
both classes. The basic idea I will pursue is that the narrow content
of a thought is given by the way that the thought divides epistemic
space: the space of epistemically possible scenarios.

We can
start by thinking about Earth and Twin Earth. Imagine that Oscar does
not know the chemical structure of the liquids in their world, but is
speculating about it. He expresses a thought by saying 'water is
XYZ'. Then Oscar's thought is false, but it is nevertheless
epistemically possible: no amount of a priori reasoning can reveal the
thought's falsity. Intuitively, the epistemic possibility of this
thought reflects the epistemic possibility of various scenarios, in
which (for example) the environment contains XYZ in the oceans and
lakes. We can say, intuitively, that Oscar's thought endorses
this sort of scenario, and that a scenario of this sort
verifies Oscar's thought. We can equally say that Oscar's
thought excludes other scenarios, in which the oceans and lakes
contain H2O, and that a scenario of this sort falsifies Oscar's
thought. So Oscar's thought seems to impose a division in epistemic
space.

One can bring out this idea as follows. Consider a
thought that the XYZ-scenario is actual: that is, that the environment
contains XYZ with a specific appearance and distribution in the oceans
and lakes. Then this thought is epistemically compatible with
Oscar's thought that water is XYZ: there is no rational inconsistency
in his accepting both. On the other hand, a thought that the
H2O-scenario is actual is epistemically incompatible with
Oscar's thought that water is XYZ: if Oscar accepts that an
H2O-scenario is actual, he should rationally reject the thought that
water is XYZ.

Note that nothing here contradicts the claims of
Kripke (1980) and Putnam (1975) that water is necessarily H2O. Kripke
allows that even if it is metaphysically impossible that water
is not H2O, it is epistemically possible that water is not H2O:
for all we know a priori, we could discover that water is XYZ. If we
discover that the XYZ-scenario is actual - that the liquids in the
oceans and lakes is XYZ, and so on - we will then be in a position to
conclude that water is XYZ. This is quite compatible with Putnam's
claim that in a counterfactual situation in which the oceans contain
XYZ, XYZ is merely watery stuff and not water. In thinking about
epistemic space, it is always epistemic possibility that is relevant.

What applies to Oscar applies also to Twin Oscar. Imagine that
Twin Oscar is in a similar position, and also expresses a thought by
saying 'water is XYZ'. Then his thought, unlike Oscar's, is true.
But more importantly here, his thought is also epistemically possible:
it endorses various epistemically possible scenarios in which the
environment contains XYZ in the oceans and lakes, and excludes others
in which the environment contains H2O. Twin Oscar's thought is
epistemically compatible with the thought that an XYZ-scenario is
actual, and it is epistemically incompatible with the thought that an
H2O-scenario is actual: if he accepts that the H2O-scenario is actual,
he should rationally reject his thought that water is XYZ. This is
the same pattern that was present for Oscar. So it seems that Oscar's
and Twin Oscar's beliefs divide epistemic space in very similar ways.

This holds out the promise that if we can make sense of the
intuitive idea of a thought's dividing epistemic space, it may yield a
notion of narrow content. To make this intuitive idea more precise,
we need to say more about the space of scenarios, and about what it is
for a scenario to be endorsed by a thought.

3 Scenarios

What is a scenario? Intuitively, a scenario corresponds to a
maximally specific epistemically possible hypothesis, such that every
epistemically possible belief is verified by at least one scenario.
One could simply postulate a space of scenarios satisfying this and
other principles; but to make the case that the notion is coherent,
and to see how scenarios behave in specific cases, it is useful to try
to construct scenarios directly from materials that are at hand.
There are two sorts of construction strategies one can appeal to here.
I have examined these at length elsewhere (Chalmers forthcoming b),
but I will say a little about them here.

The first strategy
constructs scenarios using possible worlds. Intuitively, any
possible world corresponds to a highly specific hypothesis. For any
given world W, we can entertain the hypothesis that W is
actual: that is, that our own world is qualitatively just like
W. For example, given a specific H2O-world (where the oceans contain
H2O), we can entertain the hypothesis that the H2O-world is actual:
that is, that our world is qualitatively just like the H2O-world. The
same goes for an XYZ-world. So possible worlds seem to behave at
least something like scenarios.

Possible worlds are not quite as
fine-grained as scenarios, however: an objectively specified possible
world does not correspond to a maximally specific hypothesis.
The reason is that no amount of objective information can tell me my
location within a world. Say that a world W contains XYZ in
the oceans and lakes on one planet, and H2O in the oceans and lakes on
another. Then if I know merely that W is actual, I do not know
whether my environment contains H2O or XYZ, and I do not know whether
today is Tuesday. To know these things, my location in the world must
be specified. For this reason, scenarios are better modeled by
centered worlds: worlds marked with an individual and a time as
the world's center.[*] When I consider the hypothesis that a centered
world W is actual, I consider that the world is qualitatively just
like W, that I am the individual marked at the center of W, and that
now is the time at the center. The added information given by the
center will be enough to settle the indexical claims mentioned above.

*[[See Quine 1968 and Lewis 1979. The account I
give here is very much compatible with Lewis's suggestion that belief
content should be modeled using centered worlds, although Lewis does
not ground his account in the epistemic domain.]]

One might
worry about the Kripke/Putnam point mentioned earlier. If water is
H2O in all possible worlds, how can we use possible worlds to verify a
thought that water is XYZ? But again, this worry goes away if we
think of things in terms of epistemic possibility. Consider an
XYZ-world, in which the liquid in the oceans and lakes around the
center is XYZ. Considered as a counterfactual metaphysical
possibility, one might describe this as a world in which XYZ is not
water but merely watery stuff. But considered as an epistemic
possibility, the world functions differently. Here, we consider the
hypothesis that the XYZ-world is our world: that is, the
hypothesis that our world is qualitatively just like the XYZ-world,
with XYZ in the oceans and lakes around us. When we consider this
hypothesis, as before, it verifies the thought that water is XYZ: if I
accept that the XYZ-world is my world, I should rationally accept that
water is XYZ. So the world behaves just as we wish.

This raises
an issue: in considering the hypothesis that a world W is actual, it
matters how the world is described. In effect, one considers
the hypothesis that D is the case, where D is a canonical
description of W. What is contained in the description matters:
if our description D of the XYZ-world contains "XYZ is not water",
then the hypothesis that D is the case is epistemically incompatible
with the thought that water is XYZ. To avoid this sort of thing, we
can require that canonical descriptions be restricted to a
semantically neutral vocabulary. To a first approximation, a
semantically neutral expression is one that is not susceptible to Twin
Earth thought-experiments: if corresponding semantically neutral
expressions are used by intrinsic duplicates in different
environments, they will have the same meaning.[*] Names, natural kind
terms, and demonstratives are not semantically neutral, so no such
expressions should be used in a canonical description of a world for
our purposes. What remains is a neutral vocabulary for characterizing
a world's qualitative structure. To this we can adjoin pure
indexicals such as "I" and "now", in order to specify the location of
a world's center. In this restricted vocabulary, problems of the
above sort will not arise.

*[[This first
approximation to semantic neutrality is a version of what Bealer
(1996) calls "semantic stability". For reasons discussed in Chalmers
(forthcoming a), semantic stability is not a perfect explication of
the required notion of semantic neutrality, but it is good enough for
present purposes. It should also be stipulated that to consider W as
actual is to nondeferentially consider the hypothesis that D is
the case (with a full grasp of the concepts involved in D);
deferential consideration (with an incomplete grasp) does not qualify
here.]]

The second way to deal with scenarios is to
characterize them in wholly epistemic terms, so that non-epistemic
notions of possibility are inessential to their definition. One
natural way to do this is to construct the class using
sentences in an idealized language with no expressive
limitations.[*] Here we can presuppose an epistemic necessity operator
over sentences: on the current account, S will be epistemically
necessary when it is a priori. Let us say that S and T are
epistemically equivalent when the biconditional ST is epistemically
necessary. Let us say that a sentence S leaves a sentence T open when
the conjunctions S&T and S&~T are both epistemically possible. And
let us say that a sentence is epistemically complete when it leaves no
sentence open. Then intuitively, an epistemically complete sentence
in an idealized language corresponds to a maximal epistemic
possibility. Two epistemically equivalent such sentences may
correspond to the same maximal epistemic possibility. So we can
naturally identify scenarios with equivalence classes of epistemically
complete sentences (under the epistemic equivalence relation), in the
idealized language.

What is the nature of the idealized language?
In order that the idealized language have a sentence for every
intuitive maximal epistemic possibility, we can assume that it has the
capacity for infinitary conjunctions, as well as an arbitrarily large
lexicon (subject to the following constraint). Because the
construction ascribes epistemic possibility and necessity to sentence
types rather than tokens, the vocabulary of the language must be
restricted to epistemically invariant expressions: roughly, a
vocabulary such that for any expression type in that vocabulary, all
tokens of that type have the same epistemic properties when used by
fully competent speakers. In particular, if a token of a sentence
using such a vocabulary is epistemically necessary for a fully
competent user (i.e., it expresses an epistemically necessary
thought), then any token of that sentence type is epistemically
necessary. (See Chalmers forthcoming a for more details here.)

On the epistemic construction, scenarios are tailor-made to serve as
maximal epistemic possibilities. To consider the hypothesis that a
scenario W is actual, one considers the hypothesis that D is the case,
where D is a canonical description of W. Here, a canonical
description of W is simply any of the epistemically complete sentences
in W's equivalence class. An epistemically complete claim of this
form will leave no questions open, so it will be maximally specific,
and it will be perfectly suited to model a specific location in
epistemic space.

Which of these two constructions of scenarios is
to be preferred? On my view, the two are near-equivalent: for every
scenario on the first construction, there is a corresponding scenario
on the second construction, and vice versa. However, this claim is
nontrivial, and some philosophical views will deny it. For example,
consider a theist view on which it is necessary that a god exists, but
it is not a priori that a god exists. On such a view, 'No god exists'
will be epistemically possible, and there should be maximal epistemic
possibilities involving no gods. On the epistemic construction of
scenarios, this will hold straightforwardly. But on the metaphysical
construction, there will be no such scenario: every centered world
will contain a god, so that no centered world corresponds to the
maximal epistemic possibility in question. Something similar applies
to certain philosophical views on which the laws of nature hold
necessarily: there will be epistemically possible hypotheses involving
different laws, but no centered worlds in the vicinity. And something
similar applies to certain views on which zombies and other creatures
are epistemically possible but metaphysically impossible: there will
be epistemically possible hypotheses involving zombies, but no
centered world to verify these hypotheses.

Elsewhere, I have
argued that all these views involve "strong necessities" of a sort
much stronger than the ordinary a posteriori necessities made familiar
by Kripke, and I have argued that we have no reason to believe in
them. Nevertheless, this is a substantive philosophical claim about
metaphysical possibility and necessity with which some will disagree.
For this reason, the metaphysical construction involves more
philosophical commitments than the epistemic construction, and the
latter construction is arguably more neutral. The epistemic
construction has the advantage of defining the space of scenarios in
wholly epistemic terms from the start, so that it is guaranteed to
give the right sort of epistemic results. It avoids entanglement with
issues about metaphysical possibility and necessity, and also avoids
the tricky issues about the descriptions of worlds discussed above.

For these and other reasons, I think that the epistemic
construction of scenarios is more fundamental. All the same, the
notion of a possible world is much more familiar to most philosophers,
so I will often use centered worlds to represent maximal epistemic
possibilities in what follows. When relevant issues arise, I will
indicate where how the two approaches handle them differently.

On
either approach to scenarios, there will be one scenario that is
distinguished for a given subject at a given time as the subject's
actualized scenario. On the metaphysical approach, this will
be the centered world that consists of the subject's own world,
centered on the subject at the time in question. On the epistemic
approach, this will correspond to a sentence that expresses the
complete truth about the world, from the point of view of the subject.
The subject's actualized scenario is in effect the point in a
subject's epistemic space that corresponds to reality.

On either
approach to scenarios, one can also distinguish a special class of
thoughts: the thought that a given scenario is actual. For a given
scenario W, a thought that W is actual is a thought that D is the case
(or a thought that could be expressed by uttering D), where D is a
canonical description of W. Such a thought will usually be
extraordinarily specific, and beyond the capacity of any human thinker
to think. Nevertheless, these thoughts play a useful role as a sort
of idealization in understanding the present framework.

How much
information is required to specify a scenario? That is, what is the
minimal information required for a canonical description of a
scenario? This is one of the deepest questions in philosophy, and we
do not need to take a position on it here. But it is useful to flesh
out the picture a little by considering what sort of information might
be required to specify an actualized scenario in our world,
corresponding to the complete truth about the actual world from an
individual's perspective.

First, a full description of the actual
world must include or imply the complete microphysical truth
about the world, specifying the microphysical laws and the
distribution and properties of particles, fields, and waves in space
and time. It must also include or imply the complete mental
truth about the world, specifying the conscious experiences of all
individuals at all times. On some views (e.g. some analytic
functionalist views), the mental information will itself be derivable
from the physical information, and on other views (e.g. some idealist
or phenomenalist views) the physical information will itself be
derivable from the mental information. If these views are correct,
physical or mental information alone will suffice; but if these views
are incorrect (as I think is plausible), then both sorts of
information is required to specify a maximal epistemic possibility.

The information given so far leaves open further claims about
additional material in the world: it is compatible with the
hypothesis that there is additional nonphysical, nonmental ectoplasm
in the world, for example. So assuming that no such further material
exists, the information needs to be supplemented with information
about the limits of the world: a "that's-all" clause that says
that the world contains no more than what follows from what is already
specified. Finally, all this objective information leaves open
indexical claims about the subject's own location in the world,
so it needs to be supplemented by indexical information (of the form
'I am X' and 'now is Y') specifying which individual within the world
is the subject, and what is the current time.

Elsewhere (Chalmers
and Jackson 2001; Chalmers 2002a) I have called this conjunction of
physical, mental, "that's-all", and indexical information PQTI, and
have argued that it is not implausible that PQTI epistemically
necessitates all truths about the world. If this is correct,
then PQTI itself specifies a maximal epistemic possibility, and so is
all one needs to specify one's actualized scenario. If this is
incorrect, then PQTI needs to be supplemented by further information
in order to specify a maximal epistemic possibility. We do not need
to settle this matter here, but this at least gives an illustration.

Strictly speaking, a canonical description of a scenario is
restricted to epistemically invariant terms (on the epistemic
construction) and semantically neutral terms plus indexicals (on the
metaphysical construction). It is plausible that the terms in Q, T,
and I are of the right form here. But one can argue that the
microphysical terms in P are neither epistemically invariant, nor
semantically neutral, as they are natural kind terms that involve
rigid designation and that allow epistemic differences between
individuals. So while PQTI specifies a scenario, it may not do so in
canonical form. To handle this matter, one can replace P by a
complete Ramsey-sentence formulation of its content, ultimately cashed
out in terms of causal and other lawful relations between a class of
basic elements, and causal relations to experiences. It is plausible,
although nontrivial, that one can give such a formulation in
epistemically invariant and semantically neutral terms.

More
generally, the current framework requires that one can specify any
maximal epistemic possibility using epistemically invariant terms (on
the epistemic construction) or semantically neutral terms plus
indexicals (on the metaphysical construction). This claim is again
plausible but nontrivial: one can argue for this by arguing that
epistemic variance and semantic non-neutrality in themselves give no
extra power in the specification of epistemic possibilities: at most,
they give variation between users (in the first case) and additional
power in specifying counterfactual metaphysical possibilities (in the
second case).

4 Epistemic intensions

If I had no
empirical beliefs, then the whole of epistemic space would be open to
me. With each of my empirical beliefs, the portion of epistemic space
open to me is narrowed down. Each belief endorses some scenarios, and
excludes others. When I come to believe that the earth is round,
having had no previous beliefs about the matter, I exclude a number of
scenarios that were previously open to me: scenarios involving a flat
earth or a cubical earth, for example. As more beliefs accumulate,
more scenarios are excluded. I never narrow down the class of
scenarios open to me to just one, but I may narrow down the class to a
small fraction of the original space.

This way of thinking yields
a natural conception of the content of a thought. For any thought,
there is a class of scenarios that it endorses, or equivalently a
class of scenarios that verify the thought. At the same time, there
is a class of scenarios that the thought excludes, or equivalently a
class of scenarios that falsify the thought. There may also be a
class of scenarios that the thought neither endorses nor excludes,
perhaps because they constitute borderline cases. We can think of
this division of scenarios as constituting the epistemic
content of the thought.

Let us say that two thoughts of a
subject are epistemically compatible if their conjunction is
epistemically possible, and epistemically incompatible
otherwise. One thought epistemically necessitates (or
implies) another when the first is epistemically incompatible
with the negation of the second.

What is it for a scenario to
verify a thought? Using the notions above, one can say that a
scenario W verifies a thought T when a thought that W is actual
implies T: that is, when a thought that W is actual is epistemically
incompatible with the negation of T. When this is the case, the
hypothetical assumption that W is actual will rationally lead to the
acceptance of T. One can similarly say that W falsifies T when a
thought that W is actual implies the negation of T, or when a thought
that W is actual is epistemically incompatible with T. In all these
cases, the thought that W is actual is in effect a thought that D is
the case, where D is a canonical description of W.

We can then
associate every thought with an epistemic intension. An
intension is a function from a space of possibilities of some sort to
truth-values, or to some other sort of extension. A belief's
epistemic intension is a function from scenarios to truth-values. For
a given thought T and scenario W, the epistemic intension of T is true
at W if W verifies T; the epistemic intension of T is false at W is W
falsifies T; and the epistemic intension of T is indeterminate at W if
W neither verifies nor falsifies T. I will say more about this
shortly, but first, it is useful to look at some examples. For the
purposes of these examples, I will use the understanding of scenarios
as centered worlds.

Let B1 be my belief that I am a philosopher.
Let W1 be the actual world, centered on David Chalmers, practicing
philosophy, at a certain moment in September 2001. Let W2 be a world
centered on David Chalmers at a certain time, in which he is a
mathematician, not a philosopher. Let W3 be a world centered on
Bertrand Russell in 1900, practicing philosophy. Let W4 be a world
centered on Isaac Newton in 1600, practicing mathematics but no
philosophy. All four of these correspond to epistemic possibilities,
in the broad sense: the hypothesis that W1 is actual (that is, the
hypothesis that the world is objectively like W1, and that I am the
being marked at the center, and that now is the time marked at the
center) is not ruled out a priori, and the same goes for hypotheses
concerning W2, W3, and W4.

My belief that I am a philosopher is
verified by W1 and W3. The thought that W1 is actual is epistemically
incompatible with the belief that I am not a philosopher: the
conjunction of the two can be ruled out a priori. The same goes for
W3. I can know a priori that if W1 is actual, then I am a
philosopher; and I can know a priori that if W3 is actual, then
I am a philosopher. On the other side, W2 and W4 falsify my belief
that I am a philosopher. My belief is epistemically incompatible with
the thought that W2 is actual, and with the thought that W4 is actual.
I can know a priori that if W2 is actual, then I am not a
philosopher, and I can know a priori that if W4 is actual, then
I am not a philosopher. So the epistemic intension of my belief is
true at W1 and W3, and false at W2 and W4.

To generalize: the
epistemic intension of my belief that I am a philosopher will be true
at all centered worlds where the being at the center is a philosopher,
and it will be false at all centered worlds where the being at the
center is not a philosopher. This seems to capture something about
how my belief that I am a philosopher puts epistemic constraints on
how the world might be.

Let B2 be my belief that there is water
in my pool. Let W1 be the actual world, centered on me now, with H2O
in the oceans and H2O in my pool. Let W2 be a "Twin Earth" world,
centered on my Twin Earth counterpart, where XYZ is the watery liquid
in the oceans and lakes surrounding my counterpart, and where there is
XYZ in my counterpart's pool. Let W3 be a modified Twin Earth world,
with XYZ as the watery liquid in the oceans and lakes, but where my
counterpart's pool contains no XYZ, just a small residue of H2O.

The hypothesis that W1 is actual clearly verifies B2. So does the
hypothesis that W2 is actual. The thought that W2 is actual is
epistemically incompatible with a belief that there is no water in my
pool. I can know a priori that if W2 is actual, then there is
water in my pool. On the other side, the hypothesis that W3 is actual
falsifies B2. If I accept that W3 is actual, I must rationally accept
that water is XYZ, and that there is no water in my pool. So the
epistemic intension of B2 is true at W1 and W2, but false at W3.

To generalize: the epistemic intension of my belief that there is
water in the pool is true in a centered world, very roughly, when the
dominant watery stuff in the environment of the being at the center is
present in that being's pool; and it is false, very roughly, when the
dominant watery stuff in the environment of the being at the center is
not present in that being's pool. Again, the epistemic intensions
seem to capture something about how my beliefs put epistemic
constraints on how the world might be.

Let B3 be my belief that
water is H2O, and let W1, W2, and W3 be as above. Then the thought
that W1 is actual verifies B3, but the thought that W2 is actual
falsifies B3, as does the thought that W3 is actual. I cannot
rationally accept both that W2 is actual and that water is H2O.
Indeed, if I accept that W2 is actual, I should accept that water is
XYZ. The same goes for W3. So the epistemic intension of B3 is true
at W1, but false at W2 and W3. To generalize, the epistemic intension
of my belief that water is H2O is true in a centered world, very
roughly, when the dominant watery stuff in the environment has a
certain sort of chemical structure.

Let B4 be my belief that two
plus two is four. This belief is plausibly a priori. If so, then any
scenario W verifies B4, as B4's negation is epistemically impossible.
So B4's epistemic intension is true at all scenarios. If B5 is a
belief that two plus two is five, on the other hand, then B5 can be
ruled out a priori, so B' is falsified by all scenarios. So the
epistemic intension of B5 is false at all scenarios. More generally:
any a priori belief has an epistemic intension that is true at all
scenarios, and any contradictory belief has an epistemic intension
that is false at all scenarios.

Apart from the official
definition, various heuristics can be useful in evaluating the
epistemic intension of a belief B at a scenario W. One such is the
indicative conditional heuristic suggested above by cases such
as "if W2 is actual, then there is water in my pool". This sort of
heuristic can be used be a subject to evaluate the epistemic
intensions of his or her beliefs. The heuristic is most easily
applied when a belief B is expressible by a sentence S. To evaluate
the epistemic intension of B in W, the subject can ask: if W is
actual, is S the case? This is an indicative conditional, and so
should be interpreted epistemically. (To stress the epistemic
character, one can also ask: if W turns out to be actual, will
it turn out that S?) Like other indicatives, a subject evaluates it
by the Ramsey test: one adopts the hypothesis that W is actual, and
considers whether this hypothesis rationally leads to the conclusion
that S is the case.

For example, when I adopt the hypothesis that
the Twin Earth scenario is my actual scenario - that is, that the
watery stuff in my environment is and has always been XYZ, and so on -
this rationally leads to the conclusion that water is XYZ. I can
reasonably say that if the Twin Earth scenario is actual, then
water is XYZ. Similarly, when I adopt the hypothesis that the
scenario centered on Isaac Newton is my actual scenario, this
rationally leads to the conclusion that I am a mathematician. I can
reasonably say that if the Newton scenario is my actual
scenario, than I am a mathematician.

It should be noted that a
beliefs epistemic intension involves a rational idealization. What
matters is not whether a subject would actually judge that a
belief is true, given the information that a scenario W is actual;
rather, what matters is whether a priori reasoning would allow the
subject to do in principle. Here, we idealize away from contingent
limitations on a subject's actual cognitive capacity (mistakes, memory
limitations, processing limitations, and so on), and assume the same
sort of ideal rational reflection that is invoked by the notion of
whether a claim is knowable a priori.

This idealization entails
that certain intuitive distinctions in content are lost. For example,
any a priori truth will have a necessary epistemic intension: so
assuming all mathematical truths are a priori, then they all have the
same epistemic intension. Likewise, two empirical truths that are
equivalent to each other by highly nontrivial a priori reasoning will
have the same epistemic intension. We can think of a belief's
epistemic intension as representing its ideal epistemic
content: this captures the way it constrains epistemic
possibilities when ideal reasoning is assumed. It is possible to
relax this idealization, yielding a more fine-grained notion of
epistemic content, by starting with a more demanding notion of
epistemic necessity (some details are given in Chalmers forthcoming
b).

I note also that skeptics about the a priori can define
epistemic intensions without appealing to that notion, for example by
appealing to the Ramsey-test heuristic instead, or by appealing to
another notion of epistemic necessity. On my view, the notion defined
in terms of apriority is the most fundamental here; but the general
framework is not entirely dependent on the notion of apriority, in
that one can reconstruct many of its properties without that notion.

An important note: to evaluate the epistemic intension of a
thought at a scenario W, it is not required that the thought itself be
present within W. To evaluate whether a thought is epistemically
compatible with the hypothesis that W is actual, only the original
thought is relevant; the presence or absence of thoughts in W is
usually irrelevant. For example, my belief that I am a philosopher
endorses a world centered on Nietzsche philosophizing, whether or not
he thinks that he is a philosopher. As an extreme case, it is
arguably knowable only a posteriori (through introspection and
observation) that thoughts exist, in which case a thought that there
are no thoughts is epistemically possible. Such a thought will be
verified by a scenario in which no thoughts are present. So to
evaluate a thought's epistemic intension in a scenario W, one should
not in general use the heuristic: is the thought true, as
thought in W? Instead, the evaluation is grounded in the epistemic
domain.[*]

*[[For much more on this, see Chalmers
(forthcoming a) on the distinction between "contextual" and
"epistemic" understandings of two-dimensional semantics. The current
approach is of the broadly epistemic type, which differs fundamentally
from the broadly contextual approach put forward by Stalnaker (1978)
and others. As a result, the approach here is not subject to the
problems noted by Stalnaker (1990) in using his two-dimensional
approach to yield an account of narrow content.]]

It should
be noted that epistemic content is a truth-conditional variety of
content. A thought's epistemic intension can be true in some
scenarios and false in others, and in effect, it tells us what is
required for the thought to be true, depending on which scenario turns
out to be actual. We might think of this as providing the
epistemic truth-conditions of the thought.

5 Epistemic
intensions for concepts

Thoughts are often (perhaps always)
composed from concepts. My thought that water is H2O, for
example, is plausibly composed by my concept water, my concept
H2O, and perhaps my concept of identity. As with thoughts, we
can think of a concept here as a mental token, tied to a specific
thinker. Where thoughts can be expressed by sentences, concepts can
be expressed by words and other subsentential expressions. Just as
one defines epistemic intensions for thoughts, one can also define
epistemic intensions for concepts.

Where beliefs have a
truth-value, concepts have an extension. Different sorts of
concepts have different sorts of extensions: singular concepts (such
as my concept Bill Clinton) have individuals as extensions;
general concepts (such as my concept doctor) plausibly have
classes as extensions; predicative concepts (such as hot) might
have either properties or classes as extensions, depending on how one
does things, and so on. A concept's epistemic intension will then be
a function from scenarios to extensions of the relevant type.

Formally defining a concept's epistemic intension requires some fine
details, which I will summarize briefly here (see Chalmers forthcoming
a for more). First, one has to ensure that scenarios contain entities
that can serve as extensions. On the metaphysical construction this
is automatic; on the epistemic construction, this requires some work.
We can say that two singular terms C1 and C2 are coextensive under a
scenario if a canonical description of the scenario implies 'C1=C2',
and that two singular concepts are coextensive under a scenario when a
canonical description of the scenario implies an analogous thought.
Then one can identify an individual in a scenario with an equivalence
class of epistemically invariant singular terms under that scenario.
One can analogously construct classes, properties, and the like in a
scenario, by invoking analogous notions of the coextensiveness of
general concepts, predicates, and proceeding from there. Second, one
has to identify a concept's C's extension at a scenario W. Here we
rely on concepts with which C is coextensive under W. On the
epistemic construction, C will be coextensive under W with a concept
expressible as an epistemically invariant expression B. On the
metaphysical construction, C will be coextensive under W with a
concept expressible as an expression B using only semantically neutral
terms and indexicals. Either way, B will straightforwardly pick out
an extension in W. We can then say that the epistemic intension of C
in W returns that extension.

This definition above is somewhat
technical, but the underlying notion of a concept's epistemic
intension is quite intuitive. One can get the general idea by
evaluating the epistemic intensions of one's own concepts using an
indicative-conditional heuristic. If a concept C is expressible by a
term C', we can ask: if W is actual, what is C'? (Here C' is used
rather than mentioned.)

For example, to evaluate the epistemic
intension of my concept water at the Twin Earth scenario W, I
ask: if W is actual, then what is water? The answer seems clear: if W
is actual, then water is XYZ, as before. (Or: if W turns out to be
actual, it will turn out that water is XYZ.) So at the Twin Earth
scenario, the epistemic intension of my concept water refers to
XYZ. Similarly, to evaluate the epistemic intension of my concept
I at the world W1 centered on Isaac Newton, I ask: if W1 is
actual, who am I? The answer seems clear: if W1 is actual (i.e. is
my actual world), then I am Isaac Newton. So in the Newton world, the
epistemic intension of my concept I picks out Isaac Newton.

The epistemic intension of a concept I across centered
worlds is particularly straightforward: it picks out the individual at
the center of a world. The epistemic intension of a concept
now picks out the time indicated at the center, and the
epistemic intension of a concept here picks out the location of
the individual at the time in question. As for a concept such as my
concept water: we can see that it picks out H2O in the actual
centered world, XYZ in the Twin Earth centered world, and so on.
Roughly speaking, one might say that it picks out the clear, drinkable
liquid in common use near the center of a world.

This suggests
that the epistemic intension of a concept such as my concept
water can be often be roughly encapsulated in a description.
But this sort of description is not a substitute for the intension
itself. The intension of my concept water can be evaluated at
any scenario W, by hypothetically accepting that W is actual, and
reaching rational conclusions about the nature of water under that
hypothesis. In examining cases, one can note that a given substance
seems to qualify as the extension of 'water' in a scenario in virtue
of that substance's appearance, behavior, and connection to the center
of the world; and one might try to summarize this pattern by giving a
description such as the above. But it is likely that any such
description will be at best an approximation, and in any case, a
description will only be useful insofar as it mirrors the character of
the intension. So it is the epistemic intension, not any associated
description, that has priority.

It should be noted that in some
cases, the epistemic intension of a concept expressed by a term may
vary between competent users of a term. For example, it may happen
that given complete information about a scenario, different subjects
may make different rational judgments involving the term 'water' under
that scenario. In such a case, it is plausible that the associated
concepts have different epistemic intensions. It is for this reason
that epistemic intensions are associated in the first instances with
tokens rather than types. For some expressions, epistemic intensions
might not vary between competent users in this way: examples might
include pure indexicals such as 'I', and perhaps certain descriptive
terms such as 'circular'. These expressions are precisely the
epistemically invariant expressions discussed earlier.

Any
concept of the sort that has an extension also has an epistemic
intension. This applies equally to concepts that can be expressed as
names (e.g. Gödel), as descriptions (e.g. the largest
planet in the solar system), as predicates (e.g. hot), and
so on. For any such concept, a subject who is given a full
description of a scenario is in a position to determine its extension
under that scenario. This pattern of determination corresponds to the
concept's epistemic intension.

When a concept's epistemic is
evaluated at a subject's actual scenario, it will return the
concept's actual extension. This provides a clear sense in a
concept's epistemic intension can be said to determine its
extension, in conjunction with facts about the subject's world. The
epistemic intension of a thought can be said to determine its
truth-value in the same way, in conjunction with facts about the
subject's world.

When a thought is composed of concepts, the
truth-value of the belief is usually some function of the extensions
of the concepts. For example, given a belief of the form B is
C, the belief will be true if the extensions of B and
C coincide. In such a case, the epistemic intension of the
belief will be a function of the epistemic intensions of the concepts.
At a given world, the truth-value of the belief will depend on the
extensions of the concepts by the same function according to which the
actual truth-value depends on the actual extensions. So the epistemic
intension of B is C will be true at a world if the epistemic
intensions of B and C coincide there, and so on.

As
a consequence, it is easy to see that when B is C is
epistemically necessary, B and C have the same epistemic intension.
So if we think of Hesperus as a concept whose reference is
fixed to the evening star, Hesperus is the evening star is a
priori, so Hesperus and the evening star have the same
epistemic intension. Similarly, equiangular triangle and
equilateral triangle plausibly have the same epistemic
intension (abstracting away from issues about nonEuclidean space). In
effect, a concept's epistemic intension individuates that concept up
to a priori equivalence.

6 Epistemic content is narrow

As promised, epistemic content is a sort of narrow content. This
is best illustrated by familiar examples. Consider Oscar on Earth,
and Twin Oscar on Twin Earth. Setting aside the inessential fact that
Oscar's body contains H2O and Twin Oscar's body contains XYZ, Oscar
and Twin Oscar are physical and phenomenal duplicates. Oscar and Twin
Oscar both have beliefs that they express by saying 'clouds contain
water'.

Consider the epistemic intensions of Oscar's belief B1
and Twin Oscar's beliefs B2. Let W1 be Oscar's actual scenario,
centered on Oscar with H2O around him, filling the oceans and lakes
and present in the clouds. Let W2 be Twin Oscar's actual scenario,
centered on Twin Oscar with XYZ around him, in oceans, lakes, and
clouds. Clearly, as B1 and B2 are both true, the epistemic intension
of B1 is true at W1, and the epistemic intension of B2 is true at W2.
Further, the epistemic intension of B1 is true at W2: if Oscar accepts
that W2 is actual, he should rationally accept B1. Symmetrically, the
epistemic intension of B2 is true at W1: if Twin Oscar accepts that W1
is actual, he should rationally accept B2. So the epistemic intension
of B1 is true at both W1 and W2, and so is the epistemic intension of
B2.

Something similar applies to other scenarios. Let W3 be a
scenario in which XYZ fills the oceans and lakes around the center,
but is not present in clouds (perhaps clouds merely trigger rainfall
from other invisible bodies of XYZ). If Oscar accepts that W3 is
actual, he should rationally reject his belief B1: the hypothesis that
W3 is actual is epistemically incompatible with his belief that clouds
contain water. So W3 falsifies B1. The same goes for Twin Oscar: the
hypothesis that W3 is actual falsifies his belief B2. So B1 and B2
are both false at W3.

More generally: if any scenario W verifies
Oscar's belief B1, it verifies Twin Oscar's belief B2. If W falsifies
B1, it falsifies B2. So B1 and B2 have the same epistemic intension.
At a first approximation, we can say that both of these endorse those
centered worlds in which the clear, drinkable liquid around the center
of the worlds is present in some form in the cloudlike objects around
the center of the world. This is a first approximation to the way
that this belief divides epistemic space, and it is shared between
both beliefs.

Something similar applies to any twin of Oscar.
For any such twin with corresponding belief B3, if a thought that W is
actual implies B1 for Oscar, it will imply B3 for the twin. So B3
will have the same epistemic intension as B1 and B2. So it seems that
the epistemic content of these beliefs is a sort of narrow content.

One can generalize this pattern to concepts. Take Oscar's and
Twin Oscar's water concepts. At W1, the epistemic intension of
both concepts picks out H2O. At W2, it picks out XYZ. At W3, it
picks out XYZ. At W4, a scenario in which both H2O and XYZ are
equally distributed near the center, it might pick out both. So both
concepts have the same epistemic intension. Roughly speaking, it
seems to be an epistemic intension that picks out in any given
scenario a substance in the environment of the center of the scenario,
on the basis of the substance's role and its superficial properties.

Something similar applies to any natural kind concept: there is
nothing special about water here. The same applies also to
indexical concepts. For example, both Oscar's and Twin Oscar's
I concepts pick out the individual at the center of any given
scenario, so both have the same epistemic intension. For all these
concepts, their epistemic intension is a sort of narrow content.

One can give a related analysis of the cases that Burge (1979) uses to
argue for the external nature of content. Bert, who lives in our
community, has a belief that he expresses by saying 'arthritis
sometimes occurs in the thighs'. In fact, arthritis is a disease of
the joints and cannot occur in the thigh, so it seems that Bert has a
false belief about arthritis. Twin Bert, a physical and phenomenal
duplicate of Bert, also has a belief that he expresses by saying
'arthritis sometimes occurs in the thighs'. But Twin Bert lives in a
community in which the word 'arthritis' is used for a different
disease, one that affects the muscles as well as the joints: we might
call it 'twarthritis'. It seems that Twin Bert has a true belief
about twarthritis. Where Bert believes (falsely) that he has
arthritis in his thigh, Twin Bert does not: Twin Bert believes (truly)
that he has twarthritis in his thigh. Burge concludes that in this
sort of case, belief content is not in the head.

Here, the
crucial factor is that Bert uses the term 'arthritis' with semantic
deference, intending (at least tacitly) to use the word for the
same phenomenon for which others in the community use it. If Bert
decided on his own to use the term 'arthritis' for a sort of headache,
without caring how others use the term, then his term 'arthritis'
would refer to a sort of headache, not to arthritis. With
nondeferential uses like this, one cannot construct a twin scenario of
the above sort. But with a deferential use, the content of a concept
seems to depends on practices within a subject's linguistic community,
which are themselves external to the subject.

Let B1 and B2 be
the beliefs that Bert and Twin Bert express by saying 'arthritis
sometimes occurs in the thighs'. Let V1 be Bert's actual scenario,
with a surrounding community that uses the term `arthritis' to refer
to a disease that occurs only in joints. Let V2 be Twin Bert's actual
scenario, with a surrounding community that uses the term `arthritis'
to refer to a disease that sometimes occurs in the muscles. The
epistemic intension of B1 is clearly false at V1. What about V2?
Bert can entertain the hypothesis that V2 is actual: that is, he can
entertain the hypothesis that in his community, the term `arthritis'
is used to refer to a disease of the muscles and joints. If Bert
adopts this hypothesis, then given that he uses the term `arthritis'
with semantic deference, he will rationally be led to the conclusion
that arthritis can occur in the muscles: that is, he will be led to
accept B1. In fact, for Bert, the hypothesis that V2 is actual is
epistemically incompatible with B1. So the epistemic intension of B1
is true at V2. In a similar way, the epistemic intension of B2 is
false at V1.

So the epistemic intensions of both B1 and B2 are
false at V1 and true at V2. Something similar applies to any other
scenario: when Bert and Twin Bert rationally evaluate their beliefs
under the hypothesis that a given scenario is actual, they will obtain
the same truth-value. And something similar applies to any other
duplicate of Bert or Twin Bert. For any scenario V, any such
duplicate can entertain the thought that V is actual. If such a
thought implies Bert's belief B1, such a thought will also imply the
duplicate's belief B3. So B1 and B3 have the same epistemic
intension, and once again, the belief's epistemic intension is a sort
of narrow content.

The same goes for Bert's and Twin Bert's
concepts. The epistemic intension of Bert's concept arthritis
picks out a disease of the joints in V1, and a disease of the muscles
and joints in V2. The epistemic intension of Twin Bert's concept does
the same. If one wanted to characterize the common epistemic
intension in descriptive terms, one might say very roughly that in a
given scenario, it picks out the disease referred to as `arthritis' by
speakers in the linguistic community of the individual at the center
of the scenario. This seems to roughly capture the dependence of
referent on community that semantic deference involves, and it seems
to mirror the way that Bert's and Twin Bert's beliefs will be
rationally evaluated at various epistemic possibilities.

(Of
course this sort of epistemic intension will attach only to
deferential concepts: that is, concepts expressible by terms
used with semantic deference. If an expert uses 'arthritis'
nondeferentially to refer to a certain disease of the joints, then
even if he were to accept that others use the term 'arthritis'
differently, this would not rationally lead him to reject the belief
B1 that he expresses as 'arthritis is a disease of the joints'. The
epistemic intension of his concept arthritis would pick out
(roughly) a disease of the joints in any scenario, regardless of the
way the word `arthritis' is used there.)

We can treat Putnam's
case of 'elm' and 'beech' similarly. I may know almost nothing to
distinguish elms and beeches, but my terms nevertheless refer to
different entities, through "the division of linguistic labor". In a
scenario in which the community around me refers to X-trees by 'elm',
the epistemic intension of my concept elm picks out X-trees; in
a scenario where the community refers to Y-trees by 'elm', the
epistemic intension picks out Y-trees. To characterize the epistemic
intension of my concept, we might say roughly that it picks out the
object referred to as 'elm' by the community of the individual at the
center of a given scenario. So my concepts elm and
beech will have different epistemic intensions, both narrowly
determined. As always, a concept's extension depends epistemically on
the character of the actual world; it is just that in these cases,
some of the relevant facts about the actual world are linguistic.

So far we have seen that epistemic content is narrow by looking at the
cases used to argue for wide content, and by noting that in these
cases the corresponding thoughts of intrinsic duplicates have the same
epistemic content, so that the factors responsible for the width of
some content do not affect epistemic content. To complete the case,
it would be useful to give a positive argument that epistemic content
is narrow. Such an argument requires an extended treatment, but here
I will briefly sketch how such an argument might go.

Such an
argument can proceed from two plausible theses. The first is the
thesis that epistemic necessity is narrow: that is, if a belief of a
subject is epistemically necessary, the corresponding belief of a
duplicate subject will also be epistemically necessary. Where
epistemic necessity is understood as apriority, this claim is grounded
in turn in the claim that when a subject's belief is a priori
justifiable, a duplicate's corresponding belief is also a priori
justifiable. This plausible claim is entirely unaffected by the
arguments of Putnam, Burge, and the like. If a subject's thought can
be justified by an a priori reasoning process, a corresponding thought
in a duplicate can be justified by a corresponding a priori reasoning
process.[*]

*[[One might be tempted to suggest a
Burge-like cases where a subject with incomplete competence with the
term 'bachelor' deferentially believes that bachelors are unmarried,
and a duplicate deferentially believes that all lawyers are unmarried,
and hold that the first belief is epistemically necessary but the
second is not. But as defined here, neither belief is epistemically
necessary: even the first subject's belief cannot be justified
independently of experience. At most, other (nondeferential) beliefs
in the same proposition might be epistemically necessary. Here it is
important to recall that epistemic necessity is attributed to tokens
rather than types.]]

The second is the thesis that
considering a scenario is narrow: that is, if a subject thinks a
thought that a scenario V is actual, any intrinsic duplicate of the
subject will think a corresponding thought that V is actual. Where
scenarios are understood using worlds, this follows from the fact that
the thought that V is actual is equivalent to the (nondeferential)
thought that D is the case, where D is a semantically neutral claim
that is not vulnerable to Twin-Earth-style shifts in meaning. Where
scenarios are understood using the epistemic construction, this
follows from the fact that scenarios are themselves grounded in the
narrow notions of epistemic possibility and necessity.

Given
these two theses, it is not hard to see that if one subject's thought
that V is actual epistemically necessitates a thought T, any intrinsic
duplicate has a corresponding thought that V is actual that
epistemically necessitates a corresponding thought T'. From here, it
can be seen that for any scenario V and any corresponding thoughts T1
and T2 of intrinsic duplicates, V verifies T1 iff V verifies T2. And
from this, it follows that any two corresponding thoughts of intrinsic
duplicates have the same epistemic intension. So epistemic content is
narrow.

Ultimately, the narrowness of epistemic content is
grounded in the narrowness of certain epistemic properties of
thoughts. A priori justifiability is one such property. There are
others: for example, it is plausible that if two thoughts stand in the
"Ramsey test" relation (if the first is accepted, it is rational to
accept the second), then the corresponding thoughts of any intrinsic
duplicate stand in that relation. This suggests that even without
appealing to the notion of apriority, one could use a framework of
this general sort to explicate a notion of narrow content.

7
Conclusion

How does this notion of narrow content relate to
more familiar notions of wide content? Very briefly (details are in
Chalmers 2002b): where one can define epistemic intensions in terms of
epistemic possibility and necessity, one can also define
subjunctive intensions in terms of subjunctive (or
"metaphysical") possibility and necessity. (Roughly: P is
subjunctively possible when it might have been the case that P.)
Where epistemic necessity is narrow, subjunctive necessity is often
wide; as a result, subjunctive intensions yield a sort of wide
content. This corresponds to the more familiar variety of
truth-conditional content in contemporary philosophy of language and
mind.

Any given thought has both epistemic and subjunctive
content, and these two sorts of content can be seen to co-exist
naturally in a two-dimensional approach to the content of thought and
language. One can argue that because it is constitutively tied to the
epistemic and rational domains, epistemic content has an especially
crucial role to play in the explanation of cognition and of behavior.
But that is a story to be told elsewhere.